Abstract
Models of complex systems with n components typically have order n<sup>2</sup> parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predatorprey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.
Original language  English 

Pages (fromto)  680692 
Number of pages  13 
Journal  American Naturalist 
Volume  185 
Issue number  5 
Early online date  11 Mar 2015 
DOIs  
Publication status  Published  May 2015 
Keywords
 Community matrix
 Complexity
 Food web
 Interaction strength
 Predatorprey interaction
 Stability
ASJC Scopus subject areas
 Ecology, Evolution, Behavior and Systematics
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Mark Emmerson
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